Spectral statistics of Dirac ensembles

Abstract

In this paper, we find spectral properties in the large N limit of Dirac operators that come from random finite noncommutative geometries. In particular, for a Gaussian potential, the limiting eigenvalue spectrum is shown to be universal, regardless of the geometry, and is given by the convolution of the semicircle law with itself. For simple non-Gaussian models, this convolution property is also evident. In order to prove these results, we show that a wide class of multi-trace multimatrix models have a genus expansion.